Advertisement

Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice

  • Longwen Zhou
  • Hailong Wang
  • Derek Y.H. Ho
  • Jiangbin Gong
Regular Article

Abstract

The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known Harper-Aubry-André model modified by a continuous time-periodic modulation and report on its topological properties along with several other interesting features. The Floquet bands are found to have non-zero Chern numbers which are generally different from those in the original static model. Topological phase transitions (discontinuous change of Chern numbers) take place as we tune the amplitude or period of the driving field. We demonstrate that the non-trivial Floquet band topology manifests via the quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically non-trivial Floquet bands emerge, a feature potentially useful for simulating the physics of strongly correlated systems. In some cases with an even number of Floquet bands, the spectrum features linearly dispersing Dirac cones which hold potential for the simulation of high energy physics or Klein tunnelling. Taking open boundary conditions, we observe anomalous counter-propagating chiral edge modes and degenerate zero modes. We end by discussing how these theoretical predictions may be verified experimentally.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    J.P. Dahlhaus, J.M. Edge, J. Tworzydło, C.W.J. Beenakker, Phys. Rev. B 84, 115133 (2011) ADSCrossRefGoogle Scholar
  2. 2.
    D.Y.H. Ho, J.B. Gong, Phys. Rev. Lett. 109, 010601 (2012) ADSCrossRefGoogle Scholar
  3. 3.
    T. Ozawa, I. Carusotto, Phys. Rev. Lett. 112, 133902 (2014) ADSCrossRefGoogle Scholar
  4. 4.
    M. Lababidi, I. Satija, E. Zhao, Phys. Rev. Lett. 112, 026805 (2014) ADSCrossRefGoogle Scholar
  5. 5.
    T. Oka, H. Aoki, Phys. Rev. B 79, 081406 (2009) ADSCrossRefGoogle Scholar
  6. 6.
    Z.H. Gu, H.A. Fertig, D.P. Arovas, A. Auerbach, Phys. Rev. Lett. 107, 216601 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    Á. Gómez-León, P. Delplace, G. Platero, Phys. Rev. B 89, 205408 (2014) ADSCrossRefGoogle Scholar
  8. 8.
    P. Delplace, Á. Gómez-León, G. Platero, Phys. Rev. B 88, 245422 (2013) ADSCrossRefGoogle Scholar
  9. 9.
    P.R. Lopez, J.J. Betouras, S.E. Savel’ev, Phys. Rev. B 89, 155132 (2014) ADSCrossRefGoogle Scholar
  10. 10.
    T. Iadecola, D. Campbell, C. Chamon, C.-Y. Hou, R. Jackiw, S.-Y. Pi, S.V. Kusminskiy, Phys. Rev. Lett. 110, 176603 (2013) ADSCrossRefGoogle Scholar
  11. 11.
    T. Kitagawa, T. Oka, A. Brataas, L. Fu, E. Demler, Phys. Rev. B 84, 235108 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    S. Koghee, L.-K. Lim, M.O. Goerbig, C.M. Smith, Phys. Rev. A 85, 023637 (2012) ADSCrossRefGoogle Scholar
  13. 13.
    E.S. Morell, L.E.F. Foa Torres, Phys. Rev. B 86, 125449 (2012) ADSCrossRefGoogle Scholar
  14. 14.
    P.M. Perez-Piskunow, G. Usaj, C.A. Balseiro, L.E.F. Foa Torres, Phys. Rev. B 89, 121401(R) (2014) ADSCrossRefGoogle Scholar
  15. 15.
    W. Zheng, H. Zhai, Phys. Rev. A 89, 061603 (2014) ADSCrossRefGoogle Scholar
  16. 16.
    T. Iadecola, T. Neupert, C. Chamon, Phys. Rev. B 89, 115425 (2014) ADSCrossRefGoogle Scholar
  17. 17.
    J.-I. Inoue, A. Tanaka, Phys. Rev. Lett. 105, 017401 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    N.H. Lindner, G. Refael, V. Galitski, Nat. Phys. 7, 490 (2011)CrossRefGoogle Scholar
  19. 19.
    B. Dóra, J. Cayssol, F. Simon, R. Moessner, Phys. Rev. Lett. 108, 056602 (2012) ADSCrossRefGoogle Scholar
  20. 20.
    B.M. Fregoso, Y.H. Wang, N. Gedik, V. Galitski, Phys. Rev. B 88, 155129 (2013) ADSCrossRefGoogle Scholar
  21. 21.
    J. Cayssol, B. Dóra, F. Simon, R. Moessner, Phys. Stat. Sol. RRL 7, 101C108 (2013)CrossRefGoogle Scholar
  22. 22.
    Y.T. Katan, D. Podolsky, Phys. Rev. B 88, 224106 (2013) ADSCrossRefGoogle Scholar
  23. 23.
    Y.T. Katan, D. Podolsky, Phys. Rev. Latt 110, 016802 (2013) ADSCrossRefGoogle Scholar
  24. 24.
    A. Iurov, G. Gumbs, O. Roslyak, D.H. Huang, J. Phys.: Condens. Matter 25, 135502 (2013) ADSGoogle Scholar
  25. 25.
    Y. Lumer, Y. Plotnik, M.C. Rechtsman, M. Segev, Phys. Rev. Lett. 111, 243905 (2013) ADSCrossRefGoogle Scholar
  26. 26.
    N.H. Lindner, D.L. Bergman, G. Refael, V. Galitski, Phys. Rev. B 87, 235131 (2013) ADSCrossRefGoogle Scholar
  27. 27.
    P. Titum, N.H. Lindner, M.C. Rechtsman, G. Refael, arXiv:1403.0592v1 (2014)Google Scholar
  28. 28.
    M. Pasek, Y.D. Chong, Phys. Rev. B 89, 075113 (2014) ADSCrossRefGoogle Scholar
  29. 29.
    M. Nakagawa, N. Kawakami, Phys. Rev. A 89, 013627 (2014) ADSCrossRefGoogle Scholar
  30. 30.
    L. Jiang, T. Kitagawa, J. Alicea, A.R. Akhmerov, D. Pekker, G. Refael, J.I. Cirac, E. Demler, M.D. Lukin, P. Zoller, Phys. Rev. Lett. 106, 220402 (2011) ADSCrossRefGoogle Scholar
  31. 31.
    M. Trif, Y. Tserkovnyak, Phys. Rev. Lett. 109, 257002 (2012) ADSCrossRefGoogle Scholar
  32. 32.
    M. Thakurathi, A.A. Patel, D. Sen, A. Dutta, Phys. Rev. B 88, 155133 (2013) ADSCrossRefGoogle Scholar
  33. 33.
    D.E. Liu, A. Levchenko, H.U. Baranger, Phys. Rev. Lett. 111, 047002 (2013) ADSCrossRefGoogle Scholar
  34. 34.
    Q.-J. Tong, J.-H. An, J.B. Gong, H.-G. Luo, C.H. Oh, Phys. Rev. B 87, 201109(R) (2013) ADSCrossRefGoogle Scholar
  35. 35.
    M. Thakurathi, K. Sengupta, D. Sen, arXiv:1310.4701v1 (2013)Google Scholar
  36. 36.
    C.C. Wu, J. Sun, F.J. Huang, Y.D. Li, W.M. Liu, Europhys. Lett. 104, 27004 (2013) ADSCrossRefGoogle Scholar
  37. 37.
    A. Kundu, B. Seradjeh, Phys. Rev. Lett. 111, 136402 (2013) ADSCrossRefGoogle Scholar
  38. 38.
    A.A. Reynoso, D. Frustaglia, Phys. Rev. B 87, 115420 (2013) ADSCrossRefGoogle Scholar
  39. 39.
    A.A. Reynoso, D. Frustaglia, J. Phys.: Condens. Matter 26, 035301 (2014) ADSGoogle Scholar
  40. 40.
    M. Sato, Y. Sasaki, T. Oka, arXiv:1404.2010v1 (2014)Google Scholar
  41. 41.
    Y. Li, A. Kundu, F. Zhong, B. Seradjeh, arXiv:1402.7353v1 (2014)Google Scholar
  42. 42.
    Z.-B. Wang, H. Jiang, H.W. Liu, X.C. Xie, arXiv:1404.3029v1 (2014)Google Scholar
  43. 43.
    T. Kitagawa, M.A. Broome, A. Fedrizzi, M.S. Rudner, E. Berg, I. Kassal, A. Aspuru-Guzik, E. Demler, A.G. White, Nat. Commun. 3, 882 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Y.H. Wang, H. Steinberg, P. Jarillo-Herrero, N. Gedik, Science 342, 453 (2013) ADSCrossRefGoogle Scholar
  45. 45.
    M.C. Rechtsman, J.M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, Nature 496, 196 (2013) ADSCrossRefGoogle Scholar
  46. 46.
    M.C. Rechtsman, Y. Plotnik, J.M. Zeuner, D.H. Song, Z.G. Chen, A. Szameit, M. Segev, Phys. Rev. Lett. 111, 103901 (2013) ADSCrossRefGoogle Scholar
  47. 47.
    G. Puentes, I. Gerhardt, F. Katzschmann, C. Silberhorn, J. Wrachtrup, M. Lewenstein, Phys. Rev. Lett. 112, 120502 (2014) ADSCrossRefGoogle Scholar
  48. 48.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010) ADSCrossRefGoogle Scholar
  49. 49.
    M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998) ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    T. Kitagawa, E. Berg, M. Rudner, E. Demler, Phys. Rev. B 82, 235114 (2010) ADSCrossRefGoogle Scholar
  51. 51.
    M.S. Rudner, N.H. Lindner, E. Berg, M. Levin, Phys. Rev. X 3, 031005 (2013) Google Scholar
  52. 52.
    J.K. Asbóth, H. Obuse, Phys. Rev. B 88, 121406(R) (2013) ADSCrossRefGoogle Scholar
  53. 53.
    Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993) ADSMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Y. Hatsugai, Phys. Rev. B 48, 11851 (1993) ADSCrossRefGoogle Scholar
  55. 55.
    J.K. Asbóth, Phys. Rev. B 86, 195414 (2012) ADSCrossRefGoogle Scholar
  56. 56.
    P. Leboeuf, J. Kurchan, M. Feingold, D.P. Arovas, Phys. Rev. Lett. 65, 3076 (1990) ADSMATHMathSciNetCrossRefGoogle Scholar
  57. 57.
    H.L. Wang, Derek Y.H. Ho, W. Lawton, J. Wang, J.B. Gong, Phys. Rev. E 88, 052920 (2013) ADSCrossRefGoogle Scholar
  58. 58.
    D.Y.H. Ho, J.B. Gong, arXiv:1403.7262v1 (2014)Google Scholar
  59. 59.
    K. Kudo, T.S. Monteiro, Phys. Rev. E 77, 055203 (2008) ADSCrossRefGoogle Scholar
  60. 60.
    A.R. Kolovsky, Front. Phys. 7, 3 (2012)CrossRefGoogle Scholar
  61. 61.
    P.G. Harper, Proc. Phys. Soc. London, Sect. A 68, 874 (1955)ADSMATHCrossRefGoogle Scholar
  62. 62.
    S. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 133 (1980)Google Scholar
  63. 63.
    M. Kohmoto, J. Phys. Soc. Jpn 61, 2645 (1992) ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    J. Wang, J.B. Gong, Phys. Rev. E 78, 036219 (2008) ADSCrossRefGoogle Scholar
  65. 65.
    Y.E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, O. Zilberberg, Phys. Rev. Lett. 109, 106402 (2012) ADSCrossRefGoogle Scholar
  66. 66.
    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008) ADSCrossRefGoogle Scholar
  67. 67.
    L.-J. Lang, X.M. Cai, S. Chen, Phys. Rev. Lett. 108, 220401 (2012) ADSCrossRefGoogle Scholar
  68. 68.
    D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976) ADSCrossRefGoogle Scholar
  69. 69.
    J. Wang, J.B. Gong, Phys. Rev. A 77, 031405 (2008) ADSCrossRefGoogle Scholar
  70. 70.
  71. 71.
    I. Dana, Phys. Rev. E 52, 466 (1995)ADSCrossRefGoogle Scholar
  72. 72.
    I. Dana, M. Feingold, M. Wilkinson, Phys. Rev. Lett. 81, 3124 (1998) ADSCrossRefGoogle Scholar
  73. 73.
    D.J. Thouless, Phys. Rev. B 27, 6083 (1983) ADSMathSciNetCrossRefGoogle Scholar
  74. 74.
    A. Dranov, J. Kellendonk, R. Seiler, J. Math. Phys. 39, 1340 (1998) ADSMATHMathSciNetCrossRefGoogle Scholar
  75. 75.
    A. Tanaka, M. Miyamoto, Phys. Rev. Lett. 98, 160407 (2007) ADSCrossRefGoogle Scholar
  76. 76.
    A. Tanaka, J. Phys. Soc. Jpn 80, 125002 (2011) ADSCrossRefGoogle Scholar
  77. 77.
    S.A. Parameswaran, R. Royb, S.L. Sondhi, C.R. Physique 14, 816 (2013)ADSCrossRefGoogle Scholar
  78. 78.
    E.J. Bergholtz, Z. Liu, Int. J. Mod. Phys. B 27, 1330017 (2013) ADSMathSciNetCrossRefGoogle Scholar
  79. 79.
    Z. Liu, F. Liu, Y.-S. Wu, arXiv:1404.1131v1 (2014)Google Scholar
  80. 80.
    E.L. Wolf, Graphene: A New Paradigm in Condensed Matter and Device Physics (Oxford University Press, 2014) Google Scholar
  81. 81.
    A.G. Grushin, Á. Gómez-León, T. Neupert, Phys. Rev. Lett. 112, 156801 (2014) ADSCrossRefGoogle Scholar
  82. 82.
    A. Russomanno, A. Silva, G.E. Santoro, Phys. Rev. Lett. 109, 257201 (2012) ADSCrossRefGoogle Scholar
  83. 83.
    S. Takayoshi, H. Aoki, T. Oka, arXiv:1302.4460v1 (2013)Google Scholar
  84. 84.
    Y. Hastugai, T. Fukui, H. Aoki, Phys. Rev. E 74, 205414 (2006) ADSCrossRefGoogle Scholar
  85. 85.
    J. Asbóth, L. Oroszlány, A. Pályi, Topological Insulators, p. 46, Electronic lecture notes at: http://fizipedia.bme.hu/images/1/14/Topological˙insulators.pdf

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Longwen Zhou
    • 1
  • Hailong Wang
    • 1
  • Derek Y.H. Ho
    • 1
  • Jiangbin Gong
    • 1
    • 2
  1. 1.Department of Physics and Center for Computational Science and EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.NUS Graduate School for Integrative Sciences and EngineeringSingaporeSingapore

Personalised recommendations